More simply: GaussianFace normalises each pic into a 150x120 pixel image, and uses five landmarks – two eyes, the nose, and the corners of the mouth – as the basis for the image transform. It then creates 25 x 25 overlapping tiles in the image, and captures a vector of each patch.
This sounds very much like a tweaked version of Eigenfaces.
Hey, if it works, hats off to them. After doing the Computer Vision and AI option back in uni, I'd best describe the algorithms involved in facial recognition as "bloody complex".